14Chapter33 Early Quantum theory and models of Atom

高等量子力学和量子力学的区别英文回答：The difference between advanced quantum mechanics and quantum mechanics lies in the level of complexity and mathematical formalism used in each field. Quantum mechanics is the branch of physics that describes the behavior of particles at the atomic and subatomic level. It is based on a set of mathematical principles and equations, such as the Schrödinger equation, which can be used to calculate the probabilities of different outcomes in quantum systems.Advanced quantum mechanics, on the other hand, builds upon the foundation of quantum mechanics and delves deeper into more complex and abstract concepts. It involves the study of advanced mathematical techniques, such as group theory and operator theory, to describe and analyze quantum systems. Advanced quantum mechanics also explores topics like quantum field theory, quantum information theory, andquantum many-body systems.To illustrate the difference between the two, let's consider the concept of entanglement. In quantum mechanics, entanglement refers to the phenomenon where two or more particles become linked together in such a way that the state of one particle cannot be described independently of the state of the other particles. This is famously described as "spooky action at a distance" by Albert Einstein.In advanced quantum mechanics, the study of entanglement goes beyond just understanding its existence. Researchers in this field investigate how entanglement can be used for quantum teleportation, secure communication, and quantum computing. They develop more sophisticated mathematical tools to quantify and manipulate entanglement, such as entanglement entropy and entanglement swapping.In summary, while quantum mechanics provides the foundational principles and equations for understanding the behavior of particles at the quantum level, advancedquantum mechanics takes a more advanced and mathematical approach to explore complex phenomena and applications of quantum systems.中文回答：高等量子力学和量子力学的区别在于所涉及的复杂程度和数学形式主义的使用。

Quantum entanglementMaciej LewensteinMaciej Lewenstein has obtained his degree in Physics from Warsaw University. From 1980 he worked at the Center for Theoretical Physics of the Polish Academy of Sciences. He received his doctoral degree in 1983 at the University of Essen and habilitation in 1986 in Warsaw. He became a full Professor in Poland in 1993. In 1995 he joined “Service de Photones, Atomes et Molecules” of CEA in Saclay. In 1998 he became a full professor and a head of the quantum optics theory group at the University of Hannover. In 2005 he started a new theory group at the “Insitut de Ciencias Fotoniques” in Barcelona. His research interests include: quantum optics, quantum information and statistical physics.Chiara MacchiavelloChiara Macchiavello finished her degree in Physics in 1991 and her PhD in 1995 at the University of Pavia. She held a post-doctoral for two years at the University of Oxford. Since 1998 she has been an Assistant Professor at the University of Pavia.Her research interests include quantum information processing and quantum optics.Dagmar BrussSince 2003 Dagmar Bruss is a professor at the Institute of Theoretical Physics at the University of Duesseldorf, Germany. Her research interests include the foundations of quantum information theory, classification of entanglement and quantum optical implementations of quantum computation.AbstractEntanglement is a fundamental resource in quantum information theory. It allows performing new kinds of communication, such as quantum teleportation and quantum dense coding. It is an essential ingredient in some quantum cryptographic protocols and in quantum algorithms. We give a brief overview of the concept of entanglement in quantum mechanics, and discuss the major results and open problems related to the recent scientific progress in this field.IntroductionEntanglement is a property of the states of quantum systems that are composed of many parties, nowadays frequently called Alice, Bob, Charles etc. Entanglement expresses particularly strong correlations between these parties, persistent even in the case of large separations among the parties, and going beyond simple intuition.Historically, the concept of entanglement goes back to the famous Einstein-Podolski-Rosen (EPR) “paradox”. Einstein, who discovered relativity theory and the modern meaning of causality, was never really happy with quantum mechanics. In his opinion every reasonable physical theory should exhibit a so called local realism.Suppose that we consider two particles, one of which is sent to Alice and one to Bob, and we perform independent local measurements of “reasonable” physical observables on these particles. Of course, the results might be correlated, because the particles come from the same source. But Einstein wanted really to restrict the correlations for “reasonable” physical observables to the ones that result from statistical distributions of some hidden (i.e. unknown to us and not controlled by us) variables that characterize the source of the particles. Since quantum mechanics did not seem to produce correlations consistent with a local hidden variable (LHV) model, Einstein concluded that quantum mechanics is not a complete theory. Erwin Schrödinger, in answer to Einstein’s doubts, introduced in 1935 the term “Verschränkung” (in English “entanglement”) in order to describe these particularly strong quantum mechanical correlations.Entanglement was since then a subject of intense discussions among experts in the foundations of quantum mechanics and philosophers of science (and not only science). It took, however, nearly 30 years until John Bell was able to set the framework for experimental investigations on the question of local realism. Bell formulated his famous inequalities, which have to be fulfilled in any multiparty system described by a LHV model. Alain Aspect and coworkers in Paris have demonstrated in their seminal experiment in 1981 that quantum mechanical states violate these inequalities. Recent very precise experiments of Anton Zeilinger’s group in Vienna confirmed fully Aspect’s demonstrations. All these experiments indicate the correctness of quantum mechanics, and despite various loopholes, they exclude the possibility of LHV models describing properly the physics of the considered systems.Entanglement has become again the subject of cover pages news in the 90’s, when quantum information was born. It was very quickly realized that entanglement is one of the most important resources for quantum information processing. Entanglement is a necessary ingredient for quantum cryptography, quantum teleportation, quantum densecoding, and if not necessary, then at least a much desired ingredient for quantum computing.At the same time the theory of entanglement is related to some of the open questions of mathematics, or more precisely linear algebra and functional analysis. A solution of the entanglement problem could help to characterize the so called positive linear maps, i.e. linear transformations of positive definite operators (or physically speaking quantum mechanical density matrices, see below) into positive definite operators.Entanglement of pure statesIn quantum mechanics (QM) a state of a quantum system corresponds to a vector |Psi> in some vector space, called Hilbert space. Such states are called pure states. One of the most important properties of QM is that linear superpositions of state-vectors are also legitimate state-vectors. This superposition principle lies at the heart of the matter-wave dualism and of quantum interference phenomena.Entanglement is also a result of superposition, but in the composite space of the involved parties. Let us for the moment focus on two parties, Alice and Bob. It is then easy to define states which are not entangled. Such states are product states of the form |Φ>= |a>|b>, i.e. Alice has at her disposal |a>, while Bob has |b>. Product states obviously carry no correlations between Alice and Bob. Entangled pure states may be now defined as those which are superpositions of at least two product states, such as|Φ> = α1|a1>|b1> + α2|a2>|b2> + etc.but cannot be written as a single product state in any other basis. All entangled pure states contain strong quantum mechanical correlations, and do not admit LHV models.Entanglement of mixed states and the separability problemVerify whether a given state-vector is a product state or not is a relatively easy task. In practice, however, we often either do not have full information about the system, or are not able to prepare a desired state perfectly. In effect in everyday situations we deal practically always with statistical mixtures of pure states. There exists a very convenient way to represent such mixtures as so called density operators, or matrices. A density matrix rho corresponding to a pure state-vector |Φ> is a projector onto this state. More general density matrices can be represented as sums of projectors onto pure state-vectors weighted by the corresponding probabilities.The definition of entangled mixed states for composite systems has been formulated by Reinhard Werner from Braunschweig in 1989. In fact, this definition determines which states are not entangled. Non-entangled states, called separable states, are mixtures of pure product states, i.e. convex sums of projectors onto product vectors:ρ = Σι pi|ai>|bi><ai|<bi|, (*)where 0 ≤ pi ≤ 1 are probabilities, i.e. Σιpi= 1. The physical interpretation of thisdefinition is simple: a separable state can be prepared by Alice and Bob by using local operations and classical communication. Checking whether a given state is separable or not is a notoriously difficult task, since one has to check whether the decomposition (*) exists or not. This difficult problem is known under the name of “separability or entanglement problem”, and has been a subject of intensive studies in the recent years.Simple entanglement criteriaThe difficulty of the separability problem comes from the fact that rho admits in general an infinite number of decompositions into a mixture of some states, and one has to check whether among them there exists at least one of the form (*). One of the most powerful necessary conditions for separability has been found by one of the fathers of quantum information, the late Asher Peres. Peres (Technion, Haifa) observed that since Alice and Bob may prepare separable states using local operations, Alice may safely reverse the time arrow in her system, which will change the state, but will not produce something unphysical. In general, such a partial time reversal is not a physical operation, and can transform a density operator (which is positive definite) into an operator that is no more positive definite. In fact this is what happens with all pure entangled states. Mathematically speaking partial time reversal corresponds to partial transposition of the density matrix (only on Alice's side). We arrive in this way at the Peres criterion: If a stateρis separable then its partial transposition has to be positive definite.This criterion is usually called positive partial transpose condition, or shortly PPT condition. Amazingly, the PPT condition is not only necessary for separability, but it is also a sufficient condition for low dimensional systems such as two qubits (dimension 2x2)and a system composed of one qubit and one qutrit (dimension 2x3). In higher dimensions, starting from 2x4 and 3x3, this is no longer true: there exist entangled states with positive partial transpose, which are called PPT entangled states.There exist several other necessary or sufficient separability criteria which have been established and frequently discussed in recent years. For example, states that are close to the completely chaotic state (whose density operator is equal to the normalized identity) are necessarily separable. There exist also other criteria that employ entropic inequalities, uncertainty relations, or an appropriate reordering of the density matrix (so called realignment criterion) etc. There exists, however, no general simple operational criterion of separability that would work in systems of arbitrary dimension.Entanglement witnessesThe set of all states P is obviously compact and convex. If ρ1 and ρ2are legitimate states,so is their convex mixture. The set of separable states S is also compact and convex (seeFigure 1). From the theory of convex sets and Hahn-Banach theorem we conclude that for any entangled state there exists a hyperplane in the space of operators separating rhofrom S. Such a hyperplane defines uniquely a Hermitian operator W (observable) which has the following properties: The expectation value of W on all separable states, <W> ≥ 0, whereas its expectation value on ρ is negative, i.e. <W>ρ< 0.Figure 1Such an observable is for obvious reasons called entanglement witness, since it “detects” the entanglement of ρ. Every entangled state has its witnesses; the problem obviously is to find appropriate witnesses for a given state. To find out whether a given state is separable one should check whether its expectation value is non-negative for all witnesses. Obviously this is a necessary and sufficient separability criterion, but unfortunately it is not operational, in the sense that there is no simple procedure to test for all witnesses.Nevertheless, witnesses provide a very useful tool to study entanglement, especially if one has some knowledge about the state in question. They provide a sufficient entanglement condition, and may be obviously optimized (see Figure 2) by shifting the hyperplane in a parallel way towards S.Figure 2Bell inequalitiesAfter introducing the concept of separability and entanglement for mixed states, it is legitimate to ask what is the relation of mixed state entanglement and the existence of a LHV model, which requires that the state cannot violate any of the Bell-like inequalities. Let us discuss an example of such inequalities, the so called Clauser-Horne-Shimony- Holt inequality for two qubits. Let us assume that Alice and Bob measure two binary observables each, namely A 1, A 2, and B 1, B 2. The observables are random variables taking the values +1 or − 1, correlated possibly through some dependence on local hidden variables. It is easy to see that in the classical world, if B 1 + B 2 is zero, then B 1 − B 2 is either +2 or −2, and vice versa. Therefore if we define s = A 1(B 1 + B 2 ) + A 2 (B 1 − B 2 ) , we obtain that 2 ≥ s ≥ −2. This inequality holds also after averaging over various realizations. On the other hand, it can be shown that by taking suitable sets of observables for Alice and Bob we can find pure and even mixed quantum states that violate this inequality.Are Bell-like inequalities similar in this respect to witnesses, i.e. for a given entangled state can one always find a Bell-like inequality that “detects” it? The answer to this question is no, and has been already given by R. Werner in 1989. Even for two qubits there exist entangled states that admit an LHV model, i.e. cannot violate any Bell-like inequality.This observation indicates already that there is more structure in the “eggs” of Figure 1 and Figure 2. Separable states are evidently inside the PPT egg, according to the Peres condition. They admit an LHV model, i.e. they are also inside the LHV egg. But what about PPT entangled states? Do they violate some Bell-like inequality? Peres has formulated a conjecture that this not the case, and there is a lot of evidence that this conjecture is correct, although a rigorous proof is still missing.The distillability problem and bound entanglement Above we have classified quantum states according to the property of being either separable or entangled. An alternative classification approach is based on the possibility of distilling the entanglement of a given state. In a distillation protocol the entanglement of a given state is increased by performing local operations and classical communication on a set of identically prepared copies. In this way one obtains fewer, but “more entangled”, copies. This kind of technique was originally proposed in 1996 by Bennett and coworkers in the context of quantum teleportation, in order to achieve faithful transmission of quantum states over noisy channels. It also has applications in quantum cryptography as a method for quantum privacy amplification in entanglement based protocols in the presence of noise, as pointed out by David Deutsch and coworkers from Oxford.The distillability problem poses the question whether a given quantum state can be distilled or not. A separable state can never be distilled because the average entanglement of a set of states cannot be increased by local operations. Furthermore, the positivity of the partial transpose ensures that no distillation is possible. Thus, a given PPT entangled state is not distillable, and is therefore called bound entangled. There mayeven exist undistillable entangled states which do not have the PPT property. However, this conjecture is not proved at the moment.The first example of a PPT entangled state has been found by Pawel Horodecki from Gdansk in 1997. These states are so called edge states, which means that they cannot be written as a mixture of a separable state and a PPT entangled state. Particularly simple families of states have been suggested by Charles Bennett and coworkers at IBM, New York. They have found the so called unextendible product bases (UPB), i.e. sets of orthogonal product state-vectors, with the property that the space orthogonal to this set does not contain any product vector. It turns out that the projector onto this space is a PPT state, which obviously has to be entangled since it does not contain any product vector in its range (note that all state-vectors in the decomposition of a separable state ρinto a mixture of product states belong automatically to the range of ρ).The existence of bound entanglement is a mysterious invention of Nature. It is an interesting question to ask whether bound entanglement is a useful resource to perform quantum information processing tasks. It was shown so far that this is not the case for communication protocols such as quantum teleportation and quantum dense coding (i.e.a protocol that allows to enhance the transmission of classical information, using entanglement). However, surprisingly, it is possible to distill a secret key in quantum cryptography, starting from certain bound entangled states.Entanglement detectionAs discussed above, entanglement is a precious resource in quantum information processing. Typically in a real world experiment noise is always present and it leads to a decrease of entanglement in general. Thus, it is of fundamental interest for experimental applications to be able to test the entanglement properties of the generated states. A traditional method to this aim is represented by the Bell inequalities, a violation of which indicates the presence of entanglement. However, as mentioned above, not every entangled state violates a Bell inequality. So, not all entangled states can be detected by using this method.Another possibility is to perform complete state tomography, which allows determining all the elements of the density matrix. This is a useful method to get a complete knowledge of the density operator of a quantum system, but to detect entanglement it is an expensive process as it requires an unnecessary large number of measurements. If one has certain knowledge about the state the most appropriate technique is the measurement of the witness observable, which can be achieved by few local measurements. A negative expectation value clearly indicates the presence of entanglement.All these methods have been successfully implemented in various experiments. Recently another method for the detection of entanglement was suggested based on the physical approximation of the partial transpose. It remains a challenge to implement this idea in the laboratory because it requires the implementation of non local measurements.Entanglement measuresWhen classifying a quantum state as being entangled, a natural question is to quantify the amount of entanglement it contains. For pure quantum states there exists a well defined entanglement measure, namely the von Neumann entropy of the density operator of a subsystem of the composite state. For mixed states the situation is more complicated. There are several different possibilities to define an entanglement measure. The so called entanglement cost describes the amount of entanglement one needs in order to generate a given state. An alternative measure is the entanglement of formation, which is a more abstract definition. A further possibility to quantify entanglement is given by the minimum distance to separable states. Finally, motivated by physical applications, one can introduce the distillable entanglement which quantifies the extractable amount of entanglement.Unfortunately all of these quantities are very difficult to compute in general. For example, in order to determine the entanglement of formation one has to find the decomposition of the state that leads to the minimum average von Neumann entropy of a subsystem and this is a very challenging task. So far a complete analytical formula for the entanglement of formation only exists for composite systems of two qubits.Entanglement in multipartite systemsSo far, we have restricted ourselves to the case of composite systems with two subsystems, so called bipartite systems. When considering more than two parties, i.e multipartite systems, the situation becomes much more complex. For example, for the most simple tripartite case of three qubits, a pure state can be either completely separable, or biseparable (i.e. one of the three parties is not entangled with the other two), or genuinely entangled among all three parties. The latter class again consists of inequivalent subclasses, the so called GHZ and W states. This concept can be generalized to mixed states. For more than three parties it is easy to imagine that the number of subclasses grows fast.In recent years there has been much progress in the creation of multipartite entangled states in the laboratory. The existence of genuine multipartite entanglement has also been demonstrated experimentally by using the concept of witness operators.Even if the full classification of multipartite entanglement is a formidable task, certain classes of states, the so called graph states, have been completely characterized and shown to be useful both for quantum computational and quantum error correction protocols. Moreover, a deeper understanding of entanglement has proved to be very fruitful in connection with statistical properties of physical systems. All of these problems are discussed in more details in other sections of this publication.References[1] Einstein, P. Podolsky and N. Rosen, Phys. Rev. 47, 777 (1935)[2] J.S. Bell, Physics 1, 195 (1964)[3] P. Horodecki, Phys. Lett. A 232, 333 (1997)[4] M. Lewenstein et al., J. Mod. Opt. 47, 2481 (2000)[5] A. Peres, Phys. Rev. Lett. 77, 1413 (1996)[6] E. Schrödinger, Naturwissenschaften 23, 807 (1935)[7] R.F. Werner, Phys. Rev. A 40, 4277 (1989) Contact information of the author of this article Maciej LewensteinInstitut de Ciènces Fotòniques (ICFO)C/Jordi Girona 29, Nexus 2908034 BarcelonaSpainEmail: maciej.lewenstein@icfo.esChiara MacchiavelloIstituto Nazionale di Fisicadella Materia, Unita' di Pavia Dipartimento di Fisica "A. Volta"via Bassi 6I-27100 PaviaItalyEmail: chiara@unipv.itProf. Dr. Dagmar BrussInst. fuer Theoretische Physik IIIHeinrich-Heine-Universitaet Duesseldorf Universitaetsstr. 1, Geb. 25.32D-40225 Duesseldorf,GermanyEmail: bruss@thphy.uni-duesseldorf.de。

量子场论与高等量子力学的区别Quantum field theory (QFT) and advanced quantum mechanics are two distinct branches of quantum physics, each with its own unique characteristics and applications. While both fields deal with the behavior of particles at the quantum level, they approach the subject from different angles and have distinct focuses. In this response, we will explore the differences between quantum field theory and advanced quantum mechanics from multiple perspectives.From a historical perspective, quantum mechanics was developed in the early 20th century as a framework to describe the behavior of individual particles, such as electrons and photons. It introduced concepts like wave-particle duality, quantization, and the uncertainty principle. Advanced quantum mechanics, also known as quantum mechanics beyond the introductory level, builds upon these foundational concepts and delves deeper into the mathematical formalism and applications of quantum theory.On the other hand, quantum field theory emerged in the late 1920s and early 1930s as an extension of quantum mechanics to incorporate the principles of special relativity. It treats particles as excitations of underlying fields that permeate all of spacetime. Unlike quantum mechanics, which focuses on individual particles, quantum field theory provides a framework for describing the interactions and dynamics of fields and particles in a relativistic manner.In terms of mathematical formalism, advanced quantum mechanics typically employs the Schrödinger equation or the Heisenberg picture to describe the time evolution of quantum systems. It utilizes wave functions or state vectors to represent the quantum states of particles and operators to describe observables. Quantum field theory, on the other hand, utilizes the framework of second quantization, which treats particles as quanta of field excitations. It employs field operators that create and annihilate particles and describes the state of a system using Fock space, which accounts for the presence of an arbitrary number of particles.Another key difference lies in the scope of application. Advanced quantum mechanics is often used to study systems with a small number of particles, such as atoms, molecules, and solid-state systems. It is particularly useful for understanding phenomena like quantum tunneling, energy quantization, and the behavior of particles in potential wells. Quantum field theory, on the other hand, isprimarily employed in the study of high-energy physics, where particle interactions occur at extremely small length scales and high energies. It is used to describe andpredict phenomena such as particle collisions, the behavior of elementary particles, and the creation and annihilationof particles.In summary, while both quantum field theory and advanced quantum mechanics are branches of quantum physics, they differ in their historical development, mathematical formalism, and scope of application. Quantum mechanics focuses on the behavior of individual particles and is applicable to systems with a small number of particles, while quantum field theory extends these principles toincorporate relativistic effects and describes the interactions of fields and particles in a relativistic manner, primarily in the realm of high-energy physics.。

《大西洋月刊》：美国历史上最有影响的100个名人1 Abraham LincolnHe saved the Union, freed the slaves, and presided over America’s second founding.2 George WashingtonHe made the United States possible—not only by defeating a king, but by declining to become one himself.3 Thomas JeffersonThe author of the five most important words in American history: “All men are created equal.”Louisiana purchaseEmbargo act of 1807Lewis and Clark expedition4 Franklin Delano RooseveltHe said, “The only thing we have to fear is fear itself,” and then he proved it.5 Alexander HamiltonSoldier, banker, and political scientist, he set in motion an agrarian nation’s transformation into an industrial power.6 Benjamin FranklinThe Founder-of-all-trades— scientist, printer, writer, diplomat, inventor, and more; like his country, he contained multitudes.7 John MarshallThe defining chief justice, he established the Supreme Court as the equal of the other two federal branches.8 Martin Luther King Jr.His dream of racial equality is still elusive, but no one did more to make it real.9 Thomas EdisonIt wasn’t just the lightbulb; the Wizard of Menlo Park was the most prolific inventor in American history.10 Woodrow WilsonHe made the world safe for U.S. interventionism, if not for democracy.11 John D. RockefellerThe man behind Standard Oil set the mold for our tycoons—first by making money, then by giving it away.12 Ulysses S. GrantHe was a poor president, but he was the general Lincoln needed; he also wrote the greatest political memoir in American history.13 James MadisonHe fathered the Constitution and wrote the Bill of Rights.14 Henry FordHe gave us the assembly line and the Model T, and sparked America’s love affair with the automobile.15 Theodore RooseveltWhether busting trusts or building canals, he embodied the “strenuous life” and blazed a trail for twentieth-century America.16 Mark TwainAuthor of our national epic, he was the most unsentimental observer of our national life.17 Ronald ReaganThe amiable architect of both the conservative realignment and the Cold War’s end.18 Andrew JacksonThe first great populist: he found America a republic and left it a democracy.19 Thomas PaineThe voice of the American Revolution, and our first great radical.20 Andrew CarnegieThe original self-made man forged America’s industrial might and became one of the nation’s greatest philanthropists.21 Harry TrumanAn accidental president, this machine politician ushered in the Atomic Age and then the Cold War.22 Walt WhitmanHe sang of America and shaped the country’s conception of itself.23 Wright BrothersThey got us all off the ground.24 Alexander Graham BellBy inventing the telephone, he opened the age of telecommunications and shrank the world.25 John AdamsHis leadership made the American Revolution possible; his devotion to republicanism made it succeed.26 Walt DisneyThe quintessential entertainer-entrepreneur, he wielded unmatched influence over our childhood.27 Eli WhitneyHis gin made cotton king and sustained an empire for slavery.28 Dwight EisenhowerHe won a war and two elections, and made everybody like Ike.29 Earl WarrenHis Supreme Court transformed American society and bequeathed to us the culture wars.30 Elizabeth Cady StantonOne of the first great American feminists, she fought for social reform and women’s right to vote.31 Henry ClayOne of America’s greatest legislators and orators, he forged compromises that held off civil war for decades.32 Albert EinsteinHis greatest scientific work was done in Europe, but his humanity earned him undying fame in America.33 Ralph Waldo EmersonThe bard of individualism, he relied on himself—and told us all to do the same.34 Jonas SalkHis vaccine for polio eradicated one of the world’s worst plagues.35 Jackie RobinsonHe broke baseball’s color barrier and embodied integration’s promise.36 William Jennings Bryan“The Great Commoner” lost three presidential elections, but his populism transformed the country.37 J. P. MorganThe great financier and banker was the prototype for all the Wall Street barons who followed.38 Susan B. AnthonyShe was the country’s most eloquent voice for women’s equality under the law.39 Rachel CarsonThe author of Silent Spring was godmother to the environmental movement.40 John DeweyHe sought to make the public school a training ground for democratic life.41 Harriet Beecher StoweHer Uncle Tom’s Cabin inspired a generation of abolitionists and set the stage for civil war.42 Eleanor RooseveltShe used the first lady’s office and the mass media to become “first lady of the world.”43 W. E. B. DuBoisOne of America’s great intellectuals, he made the “problem of the color line” his life’s wo rk.44 Lyndon Baines JohnsonHis brilliance gave us civil-rights laws; his stubbornness gave us Vietnam.45 Samuel F. B. MorseBefore the Internet, there was Morse code.46 William Lloyd GarrisonThrough his newspaper, The Liberator, he became the voice of abolition.47 Frederick DouglassAfter escaping from slavery, he pricked the nation’s conscience with an eloquent accounting of its crimes.48 Robert OppenheimerThe father of the atomic bomb and the regretful midwife of the nuclear era.49 Frederick Law OlmstedThe genius behind New York’s Central Park, he inspired the greening of America’s cities.50 James K. PolkThis one-term president’s Mexican War landgrab gave us California, Texas, and the Southwest.51 Margaret SangerThe ardent champion of birth control—and of the sexual freedom that came with it.52 Joseph SmithThe founder of Mormonism, America’s most famous homegrown faith.53 Oliver Wendell Holmes Jr.Known as “The Great Dissenter,” he wrote Supreme Court opinions that continue to shape American jurisprudence.54 Bill GatesThe Rockefeller of the Information Age, in business and philanthropy alike.55 John Quincy AdamsThe Monroe Doctrine’s real author, he set nineteenth-century America’s diplomatic course.56 Horace MannHis tireless advocacy of universal public schooling earned him the title “The Father of American Education.”57 Robert E. LeeHe was a good general but a better symbol, embodying conciliation in defeat.58 John C. CalhounThe voice of the antebellum South, he was slavery’s most ardent defender.59 Louis SullivanThe father of architectural modernism, he shaped the defining American building: the skyscraper.60 William FaulknerThe most gifted chronicler of America’s tormented and fascinating South.61 Samuel GompersThe country’s greatest labor organizer, he made the golden age of unions possible.62 William JamesThe mind behind Pragmatism, America’s most important philosophical school.63 George MarshallAs a general, he organized the American effort in World War II; as a statesman, he rebuilt Western Europe.64 Jane AddamsThe founder of Hull House, she became the secular saint of social work.65 Henry David ThoreauThe original American dropout, he has inspired seekers of authenticity for 150 years.66 Elvis PresleyThe king of rock and roll. Enough said.67 P. T. BarnumThe circus impresario’s taste for spectacle paved the way for blockbuster movies and reality TV.68 James D. WatsonHe codiscovered DNA’s double helix, revealing the code of life to scientists and entrepreneurs alike.69 James Gordon BennettAs the founding publisher of The New York Herald, he invented the modern American newspaper.70 Lewis and ClarkThey went west to explore, and millions followed in their wake.71 Noah WebsterHe di dn’t create American English, but his dictionary defined it.72 Sam WaltonHe promised us “Every Day Low Prices,” and we took him up on the offer.73 Cyrus McCormickHis mechanical reaper spelled the end of traditional farming, and the beginning of industrial agriculture.74 Brigham YoungWhat Joseph Smith founded, Young preserved, leading the Mormons to their promised land.75 George Herman “Babe” RuthHe saved the national pastime in the wake of the Black Sox scandal—and permanently linked sports and celebrity.76 Frank Lloyd WrightAmerica’s most significant architect, he was the archetype of the visionary artist at odds with capitalism.77 Betty FriedanShe spoke to the discontent of housewives everywhere—and inspired a revolution in gender roles.78 John BrownWhether a hero, a fanatic, or both, he provided the spark for the Civil War.79 Louis ArmstrongHis talent and charisma took jazz from the cathouses of Storyville to Broadway, television, and beyond.80 William Randolph HearstThe press baron who perfected yellow journalism and helped start the Spanish-American War.81 Margaret MeadWith Coming of Age in Samoa, she made anthropology relevant—andcontroversial.82 George GallupHe asked Americans what they thought, and the politicians listened.83 James Fenimore CooperThe novels are unreadable, but he was the first great mythologizer of the frontier.84 Thurgood MarshallAs a lawyer and a Supreme Court justice, he was the legal architect of the civil-rights revolution.85 Ernest HemingwayHis spare style defined American modernism, and his life made machismo a cliché.86 Mary Baker EddyShe got off her sickbed and founded Christian Science, which promised spiritual healing to all.87 Benjamin SpockWith a single book—and a singular approach—he changed American parenting.88 Enrico FermiA giant of physics, he helped develop quantum theory and was instrumental in building the atomic bomb.89 Walter LippmannThe last man who could swing an election with a newspaper column.90 Jonathan EdwardsForget the fire and brimstone: his subtle eloquence made him the country’s most influential theologian.91 Lyman BeecherHarriet Beecher Stowe’s clergyman father earned fame as an abolitionist and an evangelist.92 John SteinbeckAs the creator of Tom Joad, he chronicled Depression-era misery.93 Nat TurnerHe was the most successful rebel slave; his specter would stalk the white South for a century.94 George EastmanThe founder of Kodak democratized photography with his handy rolls of film.95 Sam GoldwynA producer for forty years, he was the first great Hollywood mogul.96 Ralph NaderHe made the cars we drive safer; thirty years later, he made George W. Bush the president.97 Stephen FosterAmerica’s first great songwriter, he brought us “O! Susanna” and “My Old Kentucky Home.”98 Booker T. WashingtonAs an educator and a champion of self-help, he tried to lead black America up from slavery.99 Richard NixonHe broke the New Deal majority, and then broke his presidency on a scandal that still haunts America.100 Herman MelvilleMoby Dick was a flop at the time, but Melville is remembered as the American Shakespeare.Arnold Schwarzenegger action movie actorKennedy 肯尼迪niece it is an evidence that he is a man with a strong political ambition Running for office 竞选公职Politician 政治人物California governor of a stateChief magistrate of districtCharismatic leadership 有魅力的领导Executive Charisma领袖魅力Energy and financial crisis 能源与财政危机Galileo GalileiPolitics itself is a kind of performance政治本身就是一种表演High-profile 有较高知名度的在一系列的“魔鬼”电影中，阿诺是一个仅能说“我将再来”、“再见！宝贝”或是“你被毁灭了”等简短台词、且说话带有强烈口音的肌肉男，扮演的是“魔鬼终结者”、“魔鬼毁灭者”、“最后魔鬼英雄”、“魔鬼司令”、及“终极战士”等阳刚十足的角色；在现实生活中，他是来自奥地利的移民，娶了美国前总统肯尼迪的外甥女，同时也是一位长期表达对政治有强烈企图心的名人。

原子物理与量子力学Atomic Physics and Quantum Mechanics哈尔滨理工大学应用科学学院应用物理系相关说明一、课程名称原子物理与量子力学二、计划学时108（每周3次6学时）三、课程性质技术基础课四、适用专业应用物理学、材料物理学、光信息科学与技术、电子科学与技术五、主要内容本课程内容主要可分为两大部分：1、原子物理学；2、量子力学。

原子物理学主要介绍原子物理学的发展。

从光谱学、X射线等方面的实验事实总结出能级规律，进一步分析原子结构的特点。

量子力学是二十世纪初建立起来的一门崭新的学科。

通过五个基本原理的引入，逐步构筑了量子力学的理论框架。

教学过程中，尽可能将两部分的相关内容结合讲授，利于学生理解和吸收。

原子物理学与量子力学是物理类学生的理论基础。

通过该课程的学习，学生应掌握有关原子等微观粒子的基本物理概念及反映其物理性质的基本规律，使学生了解和掌握现代一些重要的物理观念，并为应用技术准备理论基础。

六、教材与参考书《原子物理学》，褚圣麟，高教出版社《量子力学教程》，周世勋，高教出版社七、备注本课程采用多媒体教学，重点难点等采用特定的文字表现方式或动画声音等形式体现，可在“《原子物理与量子力学》课件”的相关章节观察效果。

目录绪论 (1)本章小结 (1)第一章原子的基本状况 (2)§1.1 原子的质量和大小 (2)§1.2 原子的核式结构 (2)本章小结 (3)第二章原子的能级和辐射 (4)§2.1 原子光谱的一般情况与氢原子光谱 (4)§2.2 经典理论的困难和光的波粒二象性 (4)§2.3 玻尔氢原子理论 (5)§2.4 类氢体系光谱 (5)§2.5 夫兰克-赫兹实验 (5)§2.6 量子化通则 (6)§2.7 电子的椭圆轨道 (6)§2.8 史特恩-盖拉赫实验与原子空间取向的量子化 (7)§2.9 量子理论与经典理论的对应关系对应原理 (7)本章小结 (7)第三章量子力学的运动方程—Schrödinger方程 (8)§3.1 物质的波粒二象性 (8)§3.2 波函数的统计解释 (8)§3.3 态叠加原理 (9)§3.4 薛定谔方程 (9)§3.5 几率守恒定律与定态薛定谔方程 (9)§3.6 一维无限深势阱 (10)§3.7 势垒贯穿 (10)§3.8 线性谐振子 (10)§3.9 电子在库仑场中的运动 (11)§3.10 氢原子 (11)本章小结 (12)第四章量子力学中的力学量 (13)§4.1 力学量算符 (13)§4.2 动量算符与角动量算符 (13)§4.3 厄密算符的本征函数 (14)§4.4 力学量的取值分布 (14)§4.5 算符的对易关系 (14)§4.6 测不准关系 (15)§4.7 守恒定律 (15)本章小结 (16)第五章碱金属原子的光谱和能级 (17)§5.1 碱金属原子的光谱和结构特点 (17)§5.2 碱金属原子光谱的精细结构 (17)§5.3 电子自旋与轨道运动的相互作用 (18)§5.4 单电子跃迁的选择定则 (18)*§5.5 氢原子光谱的精细结构与蓝姆移动 (18)本章小结 (19)第六章多电子原子 (20)§6.1 氦与第二族元素的光谱和能级 (20)§6.2 具有两个价电子的原子态 (20)§6.3 泡利原理与同科电子 (21)§6.4 复杂原子光谱的一般规律 (21)§6.5 辐射跃迁的普适选择定则 (21)§6.6 He-Ne激光器 (22)本章小结 (22)第七章磁场中的原子 (23)§7.1 原子的磁矩 (23)§7.2 外磁场对原子的作用 (23)§7.3 史特恩-盖拉赫实验的结果 (23)§7.4 顺磁共振 (24)*§7.5 物质的磁性 (24)§7.6 塞曼效应 (25)本章小结 (25)第八章原子的壳层结构 (26)§8.1 元素性质的周期性 (26)§8.2 原子的电子壳层结构 (26)§8.3 原子基态的电子组态 (26)本章小结 (27)第九章X射线 (28)§9.1 X射线的产生及测量 (28)§9.2 X射线的发射谱及相关能级 (28)*§9.3 X射线的吸收和散射 (28)*§9.4 X射线在晶体中的衍射 (29)本章小结 (29)第十章态和力学量的表象 (30)§10.1 态的表象 (30)§10.2 算符的矩阵表示 (30)§10.3 量子力学公式的矩阵表述 (31)§10.4 幺正变换 (31)§10.5 狄拉克符号 (31)§10.6 占有数表象 (32)本章小结 (32)第十一章微扰理论 (33)§11.1 非简并定态微扰理论及其应用 (33)§11.2 简并情况下的微扰理论及其应用 (33)§11.3 变分法与氦原子基态 (34)§11.4 与时间有关的微扰理论 (34)§11.5 跃迁几率 (34)§11.6 光的发射与吸收 (35)*§11.7 选择定则 (35)本章小结 (36)第十二章散射 (37)§12.1 碰撞过程与散射截面 (37)§12.2 中心力场中的弹性散射（分波法） (37)本章小结 (37)第十三章自旋与全同粒子 (39)§13.1 电子的自旋 (39)§13.2 电子自旋的描述 (39)§13.3 简单塞曼效应 (40)§13.4 角动量的耦合及应用 (40)§13.5 光谱的精细结构 (41)§13.6 全同粒子体系 (41)§13.7 全同粒子体系的波函数 (41)§13.8 两个电子的自旋函数 (42)本章小结 (42)绪论绪论本章主要介绍原子物理与量子力学的发展过程，并指出学习新理论应注意的问题。

量子力学英文读物以下是一些关于量子力学的英文读物推荐：1. "Quantum: Einstein, Bohr, and the Great Debate about the Nature of Reality" by Manjit Kumar2. "The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory" by Brian Greene3. "The Quantum World: Quantum Physics for Everyone" by Kenneth W. Ford4. "Quantum Mechanics: Concepts and Applications" by Nouredine Zettili5. "Quantum Physics: A Beginner's Guide" by Alastair Rae6. "Quantum Computing for Computer Scientists" by Noson S. Yanofsky and Mirco A. Mannucci7. "Quantum Physics for Babies" by Chris Ferrie (a simplified introduction for children and adults)8. "The Strange World of Quantum Mechanics" by Daniel F. Styer这些书籍从不同的角度介绍了量子力学的基本原理、应用、历史以及相关的思想争论。

根据你的兴趣和程度，选择适合你的读物开始探索量子世界吧！。

全文分为作者个人简介和正文两个部分：作者个人简介：Hello everyone, I am an author dedicated to creating and sharing high-quality document templates. In this era of information overload, accurate and efficient communication has become especially important. I firmly believe that good communication can build bridges between people, playing an indispensable role in academia, career, and daily life. Therefore, I decided to invest my knowledge and skills into creating valuable documents to help people find inspiration and direction when needed.正文：假如尼尔斯来到我们的中间英语作文500字全文共3篇示例，供读者参考篇1If Niels Bohr Came Among UsOh my gosh, can you imagine if the great Niels Bohr just randomly showed up at our school one day? That would be absolutely crazy! Niels Bohr was this brilliant physicist fromDenmark who revolutionized our understanding of atomic structure and quantum theory back in the early 20th century. He's definitely one of the most important scientists who ever lived.I've been learning all about Bohr's atomic model in physics class. It was a huge breakthrough at the time. Before Bohr, scientists kind of just accepted the plum pudding model that J.J. Thomson proposed. Basically, Thomson thought the atom was a big blob of positive charge with negative electrons scattered throughout it, kind of like raisins in a plum pudding dessert. But that didn't really fit with experimental evidence.Then Niels Bohr came along and said, "Hold up, I have a better idea!" He proposed that the atom has a positive nucleus in the center, with negative electrons orbiting around it in specific shells or energy levels. It was kind of like a tiny solar system. This atomic structure model made so much more sense and could actually explain the spectrum of light emitted by hydrogen atoms.Another huge contribution from Bohr was founding the basis for understanding quantum theory. He figured out that electrons can only exist in those discrete energy levels or shells, not just anywhere. And when they jump between those levels,that's what causes atoms to absorb or emit light of specific wavelengths. Wild, right?Bohr was awarded the Nobel Prize in Physics in 1922 for his revolutionary atomic model and work on quantum mechanics. He deserved it 100%. His insights transformed physics forever. Can you imagine if he just randomly popped into our classroom during physics period? I would be starstruck for sure!I bet Niels Bohr would blow all of our minds with his genius intellect and passionate lectures. He was totally obsessed with physics and finding the fundamental laws of the universe. I could picture him at the front of our class, messily scribbling equations on the chalkboard with chalk dust flying everywhere as he tried to explain these mind-bending quantum phenomena.Of course, he would probably get frustrated that we're still beginners struggling to understand basic concepts like atomic orbitals and blackbody radiation. "You must be joking!" he might exclaim in his thick Danish accent as we stared blankly at yet another equation he derived from first principles. I'm sure the pace of a Bohr lecture would be absolutely dizzying.At the same time, I'll bet Bohr would be an incredibly patient and caring teacher. From what I've read, he cultivated this famous "Bohr spirit" of free expression and open debate in hisresearch team. He embraced different perspectives and encouraged creative thinking. So in our classroom, Bohr would probably be very nurturing and want each of us to feel comfortable asking questions or proposing ideas, even if they seemed a bit half-baked.I could totally see him putting on a fun little demonstration to illustrate quantum principles too. Maybe he would set up a light source and use prisms or diffraction slits to show us the wave-particle duality and quantization of light. Or he might do an experiment involving atomic spectroscopy to drive home the point about discrete energy levels. Knowing Bohr, it would likely involve pipes, cables, and vacuum tubes sprawled across the lab bench in a chaotic mess that only a genius could understand. But it sure would make atomic physics feel real and alive!Just interacting with someone of Bohr's intellectual caliber and pioneering spirit would be so valuable and inspiring, even if he talked way over our heads at times. This was a man who shaped humanity's understanding of the fundamental nature of matter and energy. He wasn't afraid to challenge the status quo and think in completely new ways. That courage and creativity in the face of the unknown is what drives scientific revolutions.Part of me wonders if we mere high school students could even begin to comprehend the insights and discoveries of a mind like Niels Bohr's. His contributions to quantum theory and models of atomic structure were so profound and consequential that they're still mind-boggling a century later. Having the chance to learn from and engage with him directly would be a tremendous opportunity that could change our perspective forever.At the same time, maybe Bohr's genius wouldn't seem so alienating up close and in person. From the photos and recordings I've seen, he came across as down-to-earth, approachable, and full of playful humor despite his brilliance. Sure, he would be operating on another level intellectually. But at his core, Bohr was simply a man fascinated by the deepest mysteries of the universe, just like we kids are fascinated by even the basics of how atoms and matter work.So if Niels Bohr suddenly appeared in our classroom, I think the overall vibe would be charged with awe and excitement. This giant of 20th century science walking among us? His very presence would lend immense weight and importance to our studies of quantum phenomena. At the same time, I'm sure Bohr's warmth, passion and unwavering scientific ideals wouldinspire us to approach physics with renewed vigor and confidence in our ability to one day understand the deepest truths of nature, just like he did. It would be an unforgettable experience that could spark a lifelong love of science and discovery in all of us. I really hope it happens someday!篇2If Niles Came to Our MidstWhoa, you guys will never believe what just happened! You know that super old book we had to read for English class, A Connecticut Yankee in King Arthur's Court by Mark Twain? Well, something crazy like that totally went down at school today!It all started during Mr. Henderson's history class. We were learning about the medieval period and going over all the crazy stuff people believed back then. You know, like how they thought the world was flat and that diseases were caused by bad smells? Dumb, right?Anyway, right in the middle of Mr. H's lecture, there was this huge boom of thunder that shook the whole classroom even though it was sunny outside. Then this blinding flash of light exploded right in the center of the room. When the spots clearedfrom my eyes, there was this dude standing there dressed in the weirdest getup I've ever seen.He had on these tight leggings with a puffy shirt and this long jacket thing that went down to his knees. And get this - he was wearing tights! On his head was this funny hat with a feather sticking out the side. I thought it was bad when my little brother went through that Shakespeare phase and wouldn't stop talking in ye olde English. This guy looked like he had gone all out at one of those medieval fairs.Of course, everyone started cracking up at his ridiculous outfit. A few of the football players started chanting "Shakespeare in the park! Shakespeare in the park!" I guess they thought he was promoting some school play or something.The guy just looked around at all of us like we were the crazy ones, which made everyone laugh even harder. Finally, Mr. Henderson got the class settled down and asked the guy who he was and what he was doing here.In this super deep voice that definitely didn't match his goofy costume, he announced, "I am Niles Kalcheim, a most learned engineer from the 24th century. An unforeseen dysfunction has materialized in my chrono-displacement moduleduring its trial run, projecting me backward through thespace-time continuum."I'm not gonna lie, half of what he said went completely over my head. All I caught was "24th century" and I thought maybe this was some sort of stupid prank where one of the AV club nerds was trying to play dress up as a time traveler or something.But then the dude - Niles, I guess - went and proved he really wasn't from around here. He pulled out this shiny rectangular thing from his pocket - which actually looked kinda like one of the smartphones we're finally allowed to have at school next year. Only this one didn't have a screen or buttons or anything. It was completely smooth on both sides.Niles must have done something to activate it though because all of a sudden it projected this hologram image that hung in the air in front of him! It looked just like one of those 3D projectors they use for video games and stuff, except whatever tech he was using was a million times better. The colors were brighter and more realistic than anything I've ever seen before.The hologram was of the most bizarre contraption I've ever laid eyes on. It looked like a jungle gym designed by an insane person, with all these twisting metal tubes and giant spheres interconnected in some nutso pattern. As the hologram slowlyrotated, more and more crazy details became visible and my mind was completely blown."This is a prototype for a molecular disassembler," Niles proclaimed, like that was supposed to mean something to those of us living in the modern age rather than the 24th century.He started rambling on about how this "disassembler" could break down any object on an atomic level and convert it into elemental components or just pure energy. He claimed with enough of these crazy machines, his century had unlimited recycling and could rearrange matter itself however they wanted!Even Mr. Henderson looked dumbfounded by all this super advanced science Niles was spewing out. I figured either this guy was legitimately insane or he really was some kind of visitor from the future.That's when Niles said the words that convinced me this wasn't just an elaborate prank: "Perhaps a demonstration would render my displacement more fathomable."Before anyone could stop him, he aimed that little shiny rectangle at Mr. Henderson's desk and some kind of energy beam shot out of it. The heavy wooden desk just...disappeared!Vanished into thin air like it had never existed! All that was left behind were little sparkling particles slowly wafting through the space the desk used to occupy before they faded away completely.You can imagine the chaos that erupted after that. The girls started screaming, a few guys nearly fainted, and pretty much everyone dove for cover like Niles was about to disintegrate us all next. Even Mr. Henderson looked terrified out of his mind, sprawled there on the floor clutching his teacher's edition like it could protect him from whatever power this madman possessed.For his part, Niles just watched everyone's freaked-out reactions with an expression that seemed more confused than threatening. He tried to tell us not to be afraid, that he meant no harm, but no one was listening at that point. A few seconds later, the room was swarmed by campus security rushing in to subdue the supposed lunatic.I'm not sure what happened to Niles after that. They might have hauled him off to jail - or maybe an insane asylum is more likely considering his crazy claims of being a time traveler. Either way, I'm just glad no one else got disintegrated or anything!Can you even imagine how mind blowing it would be if Niles was telling the truth? Like, think about all the insane things wecould have in our time if his future inventions were real! Unlimited energy, the ability to just rearrange atoms however we wanted...I don't think the world today is ready for that level of technological advancement. We'd probably just use it for stupid stuff like binge watching shows without worrying about electricity bills or creating endless amounts of junk food!Still, I can't stop thinking about what might be possible in the 24th century. Just the fact that Niles could travel hundreds of years through time is crazy enough. But being able to disassemble matter into its basic components with the push of a button? If that's for real, it makes you wonder what other miraculous technologies might exist in the future. Maybe they'll have figured out how to teleport between planets or have mastered human cloning or something. Heck, maybe they'll even have figured out how to go into suspended animation so you can just sleep for 300 years and wake up in the future!Whether Niles was an actual visitor from the 24th century or just a highly convincing loon, the whole experience has me looking at the world through a different lens. For so long, our history classes have been stuck looking backward - studying the primitive civilizations, the wars and power struggles of the past. But the truth is that the most important history hasn't happenedyet. The future is where the real game-changers are going to take place that'll make everything we know today look as outdated as those eurth-cultures we learned about carving wheels out of stone.Who knows what unbelievable wonders the 24th century might hold? Flying personal vehicles, artificial intelligence assistants, maybe even some kind of master computer network safeguarding the limitless knowledge of the future! What I wouldn't give for a peek at a history book from that era. I'll bet Niles' crazy desk-dematerializer barely even registers as a significant invention compared to whatever world-altering technologies are commonplace in his time.I just hope that whoever is in charge in the 24th century uses their insane science knowledge for good and not evil. Can you imagine someone like that Thanos guy from the Avengers movies getting his hands on Niles' molecular rearranging tech? He'd be able to disassemble entire planets with the push of a button! Not that we should be worrying about hypothetical supervillains from the future, I guess. We've got enough issues to deal with in the present without borrowing troubles from another millennium.Whew, okay, that's enough of me rambling about the metaphysics of technologies yet to be invented. Whether it was real or an illusion, having a so-called time traveler materialize out of nowhere in the middle of my history class was an experience I'll never forget. It's got me thinking bigger about what might be possible and has honestly made me a lot more excited to see what the future holds - even if it's just our current century rather than the reality-bending architectures of the 24th. We're living in a pivotal time where our wildest science fictions are slowly morphing into patentable realities.Who knows? Maybe a hundred years from now, people will look back and say the real game-changing invention was whatever allowed this written record to be preserved for their eyes to read - the first relic of a primitive篇3If Niels Came Among UsBy A StudentCan you imagine what it would be like if the great Danish physicist Niels Bohr just showed up at our school one day? I've thought about this a lot, and I think it would be totallymind-blowing!First of all, I'm sure nobody would even recognize him at first. He'd probably just look like some old dude with wild Einstein hair and a funny accent. But then once the science teachers figured out who he was, it would be pure pandemonium! They'd be freaking out trying to roll out the red carpet for one of the most important scientists of the 20th century.I can just picture Niels strolling down the hallway, looking totally confused at all the commotion surrounding him. He'd probably be like "What is this peculiar place? Why are all these young people carrying those strange flat objects?" And someone would have to explain to him that we're all students at a school in the 21st century, and those "flat objects" are laptop computers that we use to access vast repositories of human knowledge and dank memes.Once he got past the initial culture shock, I bet Niels would be lowkey blown away by how much science and technology has advanced since his day. A big part of his work was on quantum theory and atomic structure, which laid the foundations for all the crazy quantum computing, nanotechnology, and other cutting-edge fields we're just starting to explore now. He'd probably get a huge kick out of seeing kids coding quantumalgorithms or running atomic force microscope simulations on their laptops.At the same time, I think he'd also be lowkey disturbed by how we sometimes take science for granted or misuse it in problematic ways. Fromatingout of more fossil fuels to industrialized warfare to social media misinformation, I can imagine Niels shaking his head and lamenting how human folly always finds new ways to run amok despite our growing scientific knowledge. He seemed like a pretty philosophical and ethical guy from what I've read, so I bet he'd want to sit us all down for some real talk about using our smarts responsibly.But more than anything, I think having Niels here would totally reinvigorate how we think about and approach science. Too often, we treat it as this dead collection of facts and formulas that we just have to regurgitate onto tests and assignments. Having one of the OG scientific revolutionaries in our midst could breathe new life into it as this radical, living endeavor to constantly question, explore, and reshape our understanding of the universe. Niels literally helped overturn centuries of classical physics doctrine, so he could show us firsthand that science isn't about memorizing - it's about creative thinking, challenging orthodoxies, and pushing the boundaries of human knowledge.I'll never forget reading about Niels's famous quote that "An expert is a person who has found out by her own painful experience all the latest mistakes." To me, that just encapsulates the mindset of a true scientist. It's all about humbly admitting the limitations of our current knowledge, while boldly venturing into new intellectual frontiers and inevitably making new mistakes that eventually lead to new discoveries. That fearless, unorthodox spirit of curiosity is what Niels embodied, and what he could hopefully instill in all of us if he walked among us.Just having a real, flesh-and-blood scientific titan like that in the classroom, wowing us with his brilliance while also showing he was still just a humble, curious human being in search of truth - it would be incredibly inspiring. We're all so used to science being this abstract collection of dusty old books and online resources. But having Niels physically present would make it more visceral and real in a whole new way. We could ask him anything we wanted about his work, his life, his mindset, his experiences - and get answers straight from the source instead of through some detached, sterilized secondhand account.Maybe Niels could even take over and lead some classes for a while, either lecturing on the latest developments in physics while he was alive or even learning about and weighing in onbrand new 21st century concepts. Just being taught by one of the most innovative scientific minds in history instead of a normal teacher would be utterly fascinating. We could get his unique perspective on not just physics, but anything from global politics to the nature of human consciousness. With Niels at the helm, our science classes would become this free-flowing Socratic dialogue where the greatest questions of the cosmos are pondered and no knowledge is too sacred to scrutinize or update as we make new empirical discoveries.Ultimately, having Niels Bohr visit our school wouldn't just be a cool celebrity cameo - it could fundamentally reshape how we experience and think about science itself. No longer would it be this dead, academic pursuit where we just absorb information. It would become an ethos - a living, evolving way of seeing and questioning the world around us with wonder, humility, and fearless curiosity. We'd go from being passive receptacles for established theories to active participants in the never-ending process of exploring, revising, and adding to human knowledge through scientific inquiry.Just picturing Niels Bohr hanging out and sharing his perspectives and life experiences with us has me brimming with excitement. Listening to that pioneering voice - the voice thathelped spark a revolutionary leap in our understanding of the universe - could imbue us with a passion for constantly questioning, challenging, and advancing our scientific narratives. We'd be connected to that grand tradition of intellectual fearlessness that shows no law or dogma is too sacrosanct once the empirical evidence points a new way. The abstract would become flesh. The dead words on a page would breathe with the vitality of the living mind that gave birth to them.Having Niels Bohr walk among us would inject a jolt of life, meaning, and inspiration into how we experience science. We'd glimpse the soul behind the formulas. We'd make a personal connection with one of the great intellectual pioneers who showed us that the universe is an ever-evolving, ever-mysterious place that constantly demands we shed our blinders and seek new truths. Just sharing the same hallways with such a luminary presence could elevate all of our scientific pursuits from rote and tedious textbook repetition to a vibrant, radical mission to boldly meet the unknown and use our minds to unravel its deepest secrets. That's what science is really about - and having Niels Bohr here could finally make us feel that in our bones.。

.量子力学专业英语词汇1、microscopic world 微观世界2、macroscopic world 宏观世界3、quantum theory 量子[理]论4、quantum mechanics 量子力学5、wave mechanics 波动力学6、matrix mechanics 矩阵力学7、Planck constant 普朗克常数8、wave-particle duality 波粒二象性9、state 态10、state function 态函数11、state vector 态矢量12、superposition principle of state 态叠加原理13、orthogonal states 正交态14、antisymmetrical state 正交定理15、stationary state 对称态16、antisymmetrical state 反对称态17、stationary state 定态18、ground state 基态19、excited state 受激态20、binding state 束缚态21、unbound state 非束缚态22、degenerate state 简并态23、degenerate system 简并系24、non-deenerate state 非简并态25、non-degenerate system 非简并系26、de Broglie wave 德布罗意波27、wave function 波函数28、time-dependent wave function 含时波函数29、wave packet 波包30、probability 几率31、probability amplitude 几率幅32、probability density 几率密度33、quantum ensemble 量子系综34、wave equation 波动方程35、Schrodinger equation 薛定谔方程36、Potential well 势阱37、Potential barrien 势垒38、potential barrier penetration 势垒贯穿39、tunnel effect 隧道效应40、linear harmonic oscillator 线性谐振子41、zero proint energy 零点能.42、central field 辏力场43、Coulomb field 库仑场44、δ-function δ-函数45、operator 算符46、commuting operators 对易算符47、anticommuting operators 反对易算符48、complex conjugate operator 复共轭算符49、Hermitian conjugate operator 厄米共轭算符50、Hermitian operator 厄米算符51、momentum operator 动量算符52、energy operator 能量算符53、Hamiltonian operator 哈密顿算符54、angular momentum operator 角动量算符55、spin operator 自旋算符56、eigen value 本征值57、secular equation 久期方程58、observable 可观察量59、orthogonality 正交性60、completeness 完全性61、closure property 封闭性62、normalization 归一化63、orthonormalized functions 正交归一化函数64、quantum number 量子数65、principal quantum number 主量子数66、radial quantum number 径向量子数67、angular quantum number 角量子数68、magnetic quantum number 磁量子数69、uncertainty relation 测不准关系70、principle of complementarity 并协原理71、quantum Poisson bracket 量子泊松括号72、representation 表象73、coordinate representation 坐标表象74、momentum representation 动量表象75、energy representation 能量表象76、Schrodinger representation 薛定谔表象77、Heisenberg representation 海森伯表象78、interaction representation 相互作用表象79、occupation number representation 粒子数表象80、Dirac symbol 狄拉克符号81、ket vector 右矢量82、bra vector 左矢量83、basis vector 基矢量84、basis ket 基右矢85、basis bra 基左矢.86、orthogonal kets 正交右矢87、orthogonal bras 正交左矢88、symmetrical kets 对称右矢89、antisymmetrical kets 反对称右矢90、Hilbert space 希耳伯空间91、perturbation theory 微扰理论92、stationary perturbation theory 定态微扰论93、time-dependent perturbation theory 含时微扰论94、Wentzel-Kramers-Brillouin method W. K. B.近似法95、elastic scattering 弹性散射96、inelastic scattering 非弹性散射97、scattering cross-section 散射截面98、partial wave method 分波法99、Born approximation 玻恩近似法100、centre-of-mass coordinates 质心坐标系101、laboratory coordinates 实验室坐标系102、transition 跃迁103、dipole transition 偶极子跃迁104、selection rule 选择定则105、spin 自旋106、electron spin 电子自旋107、spin quantum number 自旋量子数108、spin wave function 自旋波函数109、coupling 耦合110、vector-coupling coefficient 矢量耦合系数111、many-particle system 多子体系112、exchange forece 交换力113、exchange energy 交换能114、Heitler-London approximation 海特勒-伦敦近似法115、Hartree-Fock equation 哈特里-福克方程116、self-consistent field 自洽场117、Thomas-Fermi equation 托马斯-费米方程118、second quantization 二次量子化119、identical particles 全同粒子120、Pauli matrices 泡利矩阵121、Pauli equation 泡利方程122、Pauli’s exclusion principle泡利不相容原理123、Relativistic wave equation 相对论性波动方程124、Klein-Gordon equation 克莱因-戈登方程125、Dirac equation 狄拉克方程126、Dirac hole theory 狄拉克空穴理论127、negative energy state 负能态128、negative probability 负几率129、microscopic causality 微观因果性.。

光线的研究英语课文The history of light research, like optics and mechanics, was noticed in ancient Greece, and the law of light reflection was well known as early as Euclid's time. However, before the separation of natural science and religion, human understanding of the nature of light hardly made any progress, and only stayed at the level of understanding the forms of light transmission and application. In the 17th century, there were two kinds of voices about this problem: the wave theory and the particle theory.The Dutch physicist Huygens put forward the wave theory of light in his book "On Light" published in 1690, and deduced the law of reflection and refraction of light, which satisfactorily explained the reason why the speed of light decreased in dense medium, and at the same time explained the birefringence phenomenon when light entered ice.Newton, a British physicist, insisted on the theory of light particles. In his book Optics published in 1704, he proposed that light-emitting objects emit particles moving in a straight line, and the flow of particles hitting the retina will cause vision, which can also explain the refraction and reflection of light, and even the modification can explain thephenomenon of "diffraction" discovered by grimaldi.In 19th century, British physicist Maxwell introduced the concept of displacement current, established the basic equation of electromagnetism, and founded the electromagnetic theory of light. By proving that the speed of electric microwave propagating in vacuum is equal to the speed of light propagating in vacuum, it is deduced that light and electromagnetic wave are essentially the same, that is, light is an electromagnetic wave with a certain wavelength. In the 20th century, quantum theory and relativity were established one after another, and physics changed from classical physics to modern physics. In 1905, American physicist Einstein put forward the famous photoelectric effect.He believed that when ultraviolet rays irradiated the surface of an object, they would transfer energy to the surface electrons, so that they could get rid of the shackles of the nucleus and be released from the surface. Therefore, Einstein interpreted light as a collection of energy, photons. In 1925, the French physicist De Broglie put forward the theory that all substances have wave-particle duality, that is, all objects are both waves and particles. Then, several scientists, such as Planck, a famous German physicist, established the quantumphysics theory, which completely expanded human understanding of material properties. To sum up, the essence of light should be considered as "photon", which has wave-particle duality. Therefore, light is both a wave and a photon, but as a unique substance, its volatility still dominates. At the same time, light has dynamic mass, and its mass can be calculated according to Einstein's mass-energy equation.。

英文原版薛定谔科普Quantum mechanics, as proposed by Austrian physicist ErwinSchrödinger, is a fundamental theory in physics that describes the behavior of particles at the smallest scales. It provides a mathematical framework for understanding the wave-particle duality of matter and the probabilistic nature of physical interactions. Although quantum mechanics is widely considered to be one of the most successful theories in science, it is also one of the most perplexing and counterintuitive.量子力学是由奥地利物理学家薛定谔提出的一种基本理论，描述了粒子在最小尺度上的行为。

它为理解物质的波粒二象性和物理相互作用的概率性提供了数学框架。

虽然量子力学被广泛认为是科学中最成功的理论之一，但也是最令人困惑和反直觉的。

One of the fundamental principles of quantum mechanics is the superposition principle, which states that a system can exist in multiple states simultaneously until it is measured. This idea challenges our classical understanding of physical reality, where objects are expected to have definite properties at all times. Thefamous thought experiment known as Schrödinger's cat illustrates this concept, where a cat trapped in a box is considered both alive and dead until the box is opened and observed.量子力学的一个基本原理是叠加原理，它表明一个系统可以同时存在多个状态，直到被测量出来。